1. Consider two machines that are maintained by a single repair- man. Machineifunctions for an exponentially distributed amount of time with rateibefore it fails. The repair times for each unit are exponential with ratei. They are repaired in the order in which they fail. Formulate a Markov chain model for this situation with state space{0,1,2,12,21}and write down the matrix of transition rates.
2. In the previous problem suppose that1=2=1=2= 1. Suppose that the system starts off with the uniform distribution over{0,1,2,12,21}. Show that at each later moment it is again in each state with equal probability